diff --git a/var/spack/repos/builtin/packages/intel-oneapi-compilers-classic/package.py b/var/spack/repos/builtin/packages/intel-oneapi-compilers-classic/package.py
index 1b81e0ff63..7622b6aed8 100644
--- a/var/spack/repos/builtin/packages/intel-oneapi-compilers-classic/package.py
+++ b/var/spack/repos/builtin/packages/intel-oneapi-compilers-classic/package.py
@@ -36,6 +36,9 @@ class IntelOneapiCompilersClassic(Package):
         version(ver)
         depends_on("intel-oneapi-compilers@" + oneapi_ver, when="@" + ver, type="run")
 
+    # icc@2021.6.0 does not support gcc@12 headers
+    conflicts("%gcc@12:", when="@:2021.6.0")
+
     @property
     def oneapi_compiler_prefix(self):
         oneapi_version = self.spec["intel-oneapi-compilers"].version